Question

michael owes his parents a bunch of money. five out of every six dollars of his total debt came about because of the time last summer when he tried to drive the snowmobile across mud lake. it didn’t end well.
define units for michael’s total debt and the amount michael owes because of the snowmobile incident.
1 if michael’s total debt to his parents is six hundred dollars, how much does he owe his parents for repairs due to the snowmobile incident?
2 if michael’s total debt to his parents is $450, how much does he owe his parents?
(there is also a chart titled from snowmobile (dollars) with a grid and some plotted points, and a table with columns for question 2, question 3, and expression, with values 450, 375, etc.)

Explanation:

Step1: Analyze the problem (Question 1)

We know the total debt is six hundred dollars (\(600\) dollars) and we need to find the debt due to the snowmobile incident. Wait, maybe there's a ratio or fraction? Wait, the table has 450 and 375? Wait, maybe the first part: "five out of every six dollars of his total debt came about because of the time last summer..." Wait, maybe the total debt is 600, and the fraction for the snowmobile incident? Wait, maybe the problem is: Michael's total debt to parents is 600 dollars. Five out of every six dollars is from other, and one out? Wait, no, let's re-read. "five out of every six dollars of his total debt came about because of the time last summer... the snowmobile incident" Wait, maybe the total debt is 600, and the debt due to snowmobile is total debt times (1 - 5/6)? Wait, no, maybe the first question: "If Michael’s total debt to his parents is six hundred dollars, how much does he owe his parents for repairs due to the snowmobile incident?" So total debt \(T = 600\) dollars. The problem says "five out of every six dollars of his total debt came about because of the time last summer...", so the debt due to snowmobile is total debt minus (5/6 of total debt), or (1/6) of total debt? Wait, 5 out of 6 is other, so 1 out of 6 is snowmobile. So calculate \(600\times\frac{1}{6}\).

Step2: Calculate the debt for snowmobile (Question 1)

Total debt \(T = 600\) dollars. Fraction for snowmobile incident: \(1 - \frac{5}{6}=\frac{1}{6}\) (since 5/6 is other). So debt for snowmobile: \(600\times\frac{1}{6} = 100\) dollars? Wait, but the table has 450 and 375. Wait, maybe Question 2: "If Michael’s total debt to his parents is $450, how much does he owe his parents?" Wait, no, Question 2: "If Michael’s total debt to his parents is $450, how much does he owe his parents (for snowmobile? Or total? Wait, the table has 450 and 375. Wait, maybe the ratio is 5/6 for other, 1/6 for snowmobile. So for total debt \(T\), snowmobile debt is \(T\times\frac{1}{6}\), other is \(T\times\frac{5}{6}\). Let's check Question 2: If total debt is 450, then snowmobile debt is \(450\times\frac{1}{6}=75\)? But the table has 375. Wait, 450 - 75 = 375. Oh! So other debt is \(450\times\frac{5}{6}=375\), and snowmobile is 75. So Question 1: total debt 600, snowmobile debt is \(600\times\frac{1}{6}=100\), other is \(600\times\frac{5}{6}=500\). Question 2: total debt 450, snowmobile debt is \(450\times\frac{1}{6}=75\), other is 375 (which matches the table).

So let's solve Question 1:

Total debt \(T = 600\) dollars.

Fraction for snowmobile incident: \(\frac{1}{6}\) (since 5/6 is other).

Debt for snowmobile: \(600\times\frac{1}{6}=100\) dollars.

For Question 2:

Total debt \(T = 450\) dollars.

Fraction for snowmobile incident: \(\frac{1}{6}\), so debt is \(450\times\frac{1}{6}=75\) dollars? Wait, but the table has 375 as other, which is \(450\times\frac{5}{6}=375\), so snowmobile is 450 - 375 = 75.

But let's focus on Question 1 first.

Step1 (Question 1): Identify the fraction

Total debt: 600 dollars.

Fraction of debt due to snowmobile: \(1 - \frac{5}{6}=\frac{1}{6}\) (since 5/6 is from other causes).

Step2 (Question 1): Calculate the debt

Debt = \(600\times\frac{1}{6}=100\) dollars.

For Question 2:

Step1 (Question 2): Identify total debt and fraction

Total debt: 450 dollars.

Fraction of debt due to snowmobile: \(\frac{1}{6}\).

Step2 (Question 2): Calculate the debt

Debt = \(450\times\frac{1}{6}=75\) dollars. Or, since other debt is 375, debt = 450 - 375 = 75.

Answer:

(Question 1):
100 dollars